Jeremy Corbyn called on Labour MPs to “end the trench warfare” and get behind a socialist vision for Britain under which he would allow councils to borrow more, raise taxes on business to fund education and suspend arms sales to Saudi Arabia.

Corbyn's relaunch and Labour's conference – Politics Weekly podcast

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Setting out a radical leftwing agenda that secured rapturous applause from supporters in the hall in Liverpool but a sceptical response from some Labour MPs, Corbyn also hit back at party critics who say he is uninterested in winning elections.

“Yes, our party is about campaigning and it’s about protest too but most of all it’s about winning power in local and national government to deliver the real change our country so desperately needs,” he said, describing his vision as “21st-century socialism”.

The Labour leader did admit that his party had to face up to the challenge of Brexit and said it had an “electoral mountain to climb”. But he added that the party needed to come together to take on Theresa May’s Conservatives.

“Let’s be frank, no one will be convinced of a vision promoted by a divided party. We all agree on that. So I ask each and every one of you – accept the decision of the members, end the trench warfare and work together to take on the Tories,” he said.

The party leader, in his second keynote address to conference as leader, used the opportunity to set out key policies to the conference including:

Scrapping the local borrowing cap, which would allow councils to use their existing housing stock to raise money that could be ploughed back into council housebuilding.

Raising corporation tax by up to 1.5% to fund an education maintenance allowance for college students as part of a national education service.

Banning arm sales where there are credible reports of human rights abuses or war crimes being committed “starting with Saudi Arabia”, which he said committed repeated violations of international humanitarian law and war crimes.

He said he had laid down his policy vision in a document that had been accepted by Labour’s national executive committee. But in a joke aimed at those who talk of a “cult of Corbyn”, he added: “Don’t worry, they’re not the Ten Commandments. They will now go to the national policy forum and the whole party needs to build on them, refine them and, above all, take them out to the people of this country.”

One of the loudest and longest cheers during the speech was when he told the audience that he believed recent wars had spread terrorism, sectarianism and violence.

“That is why it was right to apologise on behalf of the party for the Iraq war, right to say that we have learned the lessons, and right to say that such a catastrophe must never be allowed to happen again,” said Corbyn, causing most of the audience to rise to its feet but a few members to walk out in what could be seen as an attack of the former Labour leader, Tony Blair.

Many MPs think Corbyn’s leftwing vision cannot win an election because they believe it will not appeal to people who voted Conservative in 2015. But his supporters argue that his victory among members and registered supporters has earned him the right to carry his package into an election.

The speech was in stark contrast to that delivered by the deputy leader, Tom Watson, on Tuesday in which he urged delegates to stop “trashing the record” of Blair and Gordon Brown – and argued that capitalism is not the enemy.

In his speech, Corbyn seemed to counter Watson’s point. He said: “The global banking crash is an object lesson of out-of-control greed and speculation that crashed economies across the globe and required the biggest ever government intervention and public bailout in history.”

Corbyn used his speech to pay tribute to Labour MP Jo Cox, who was killed outside her constituency office, and address the spate of abuse and hate that he called “utterly unacceptable”.

The Labour leader then provided his strongest response yet on the issue of antisemitism, describing it as “evil” and as having led to the worst crimes of the 20th century. “This party always has and always will fight against prejudice and hatred of Jewish people with every breath in its body,” he said.

However, the comments came as Momentum’s vice chair, Jackie Walker, came under pressure to resign after she incorrectly criticised Holocaust Memorial Day at a party antisemitism training session for commemorating only Jewish victims.

Walker took issue with the definition of antisemitism used at the training event, which was organised for members at the party conference by the Jewish Labour Movement (JLM).

“In terms of Holocaust day, wouldn’t it be wonderful if Holocaust day was open to all people who experienced Holocaust?” she told organisers, heard in a recording of the event.

Holocaust Memorial Day is intended to commemorate all victims of the Nazi Holocaust, and other genocides, including atrocities in Bosnia and Rwanda.

After shouts from participants, Walker said that was not how she viewed the event. “In practice, it’s not actually circulated and advertised as such,” she said. “I was looking for information and I still haven’t heard a definition of antisemitism that I can work with.”

She later said in a statement: “I would never play down the significance of the Shoah. Working with many Jewish comrades, I continue to seek to bring greater awareness of other genocides, which are too often forgotten or minimised. If offence has been caused, it is the last thing I would want to do and I apologise.”

Walker, who is an old friend of Corbyn’s, was previously suspended from the Labour party after posting during a Facebook discussion that Jews were “chief financiers of the sugar and slave trade” and arguing “the Jewish Holocaust does not allow Zionists to do what they want”. She was readmitted to the party after an investigation.

Corbyn used the speech to stamp down his authority by offering no apology for his pro-immigration stance.

Faced with criticism from Labour colleagues who believe he is offering the wrong response to the Brexit vote, he said: “It isn’t migrants that drive down wages ... It isn’t migrants who put a strain on our NHS ... It isn’t migrants that have caused a housing crisis.”

MP Stephen Kinnock MP said the speech was strong on the economy and innovation but added: “The challenge now is to do more to reassure the British people that Labour is strong on defence and security, and we must also develop policies on immigration that better reflect people’s very real and legitimate concerns about free movement.”

Corbyn’s speech drew an end to the conference, which began with him securing 61.8% of the vote in his battle with Owen Smith.